Post on 11-Mar-2018
Scanning Gate Microscopy of the
QSH edge states Markus König, Andrei Garcia, David Goldhaber-Gordon
Stanford University
Christoph Brüne, Hartmut Buhmann, Laurens Molenkamp Universität Würzburg
-2,0 -1,5 -1,0 -0,5 0,0102
103
104
105
106
107
G = 2 e2/h
G = 0.005 e2/h
Rxx
/ Ω
Vg / V
45 Å 80 Å
Demonstration of QSHE in HgTe quantum wells
Present experimental results
Transport based on edge states
-2.5 -2.0 -1.5 -1.0 -0.5 0.00
2
4
6
8
10
5
10
15
20
25
R14
,23 (k
Ω)
Vgate (V)
I (n
A)
LB 6.4 kΩ
M. König et al., Science 318, 766 (2007)
Present experimental results (2)
inelastic scattering magnetic field
Conductance is suppressed by
-2,0 -1,5 -1,0 -0,5 0,0102
103
104
105
106
107
G = 2 e2/h
G = 0.005 e2/h
Rxx
/ Ω
Vg / V
45 Å ( 1 µm x 1 µm) 80 Å (20 µm x 13 µm) 80 Å ( 1 µm x 1 µm)
G = 0.25 e2/h
-0,10 -0,05 0,00 0,05 0,100,0
0,2
0,4
0,6
0,8
1,0
90° 75° 60° 45° 30° 15° 10° 5° 0° G
norm
B / T
α
B
mean free path ~ 1 μm field strength ~ 10 mT
Open questions
Edge states: spatial arrangement width (Zhou et al., PRL (2008))
Stability of QSH state: Scattering due to potential fluctuations Breaking time reversal symmetry in B-field
Scanning Gate Microscopy
M.A. Topinka et al., Nature 410, 183 (2001)
M. Jura et al., Nature Physics 3, 841 (2007)
Basic SGM principles
tip potential induces perturbation leads to backscattering
decrease of conductance can be detected ΔG = 0
ΔG = 0
ΔG < 0
Application to QSH states
tip acts like local top gate potential fluctuation within the QSH regime Fermi level locally in conduction (valence) band
potential fluctuation can cause backscattering backscattering decreases conductance (only scattering into counter-propagating state)
G = 2e2/(3h)
Tip-induced scattering
Scattering mechanisms: 2D reservoirs Kondo impurities
2D reservoirs scattering sets in at critical Vtip
G saturates at predictable value Kondo-like impurities
scattering depends on occupation of impurity transition to 2D island for large impurity
G = 2e2/h
Spatial mapping
AFM as complementary technique low-T AFM: in-situ comparison of transport results to spatial properties room-T AFM: high resolution of edge profile
details of scattering might affect results
Kondo: range of interaction? 2D island: size critical lower spatial resolution
spatial extension of edge states
Detailed study of scattering
sensitivity to potential fluctuations
dominant mechanism?
compensate intrinsic fluctuations for larger samples: G0 < 2 e2/h remove single perturbation by suitable tip potential
QSH states in magnetic field
low B: no full suppression of G high B: reentrant QH state
-0,10 -0,05 0,00 0,05 0,100,0
0,2
0,4
0,6
0,8
1,0
90° 75° 60° 45° 30° 15° 10° 5° 0° G
norm
B / T
α
B
0 2 4 6 8
-30
-20
-10
0
10
20
30
B / T
Rxy
/ kΩ
0,5 1,0 1,5 2,0 2,5 3,00
5
10
15
20
25
30
35
40
R /
kΩ
B / T
Tracking the states in high B-field
different scattering mechanisms (B vs. Vtip) tip perturbation leads to further decrease of
conductance change in sensitivity to tip perturbation? clear connection of QSHE and re-entrant QHE
σxy = e²/h σxy = 0 σxy = 0
Magnetic perturbation
commercial MFM tips: several 10 mT homogeneous perpendicular field: significant suppression for B = 10 mT effect of local field comparable? spatial variation of B-field effect?
dependence on intrinsic potential fluctuations increased sensitivity
combination of magnetic and electric perturbation
Summary
Scanning Gate Microscopy useful for more detailed characterization of QSH states spatial mapping scattering mechanisms
2D islands Kondo impurities breaking time reversal symmetry
behavior in high magnetic fields